Compressed sensing (CS) is a new sampling theory and has become a major research direction in applied mathematics in the last 10 years. The key idea of CS for addressing the big data problem is to avoid sampling data that can be recovered afterwards. However, mathematical recovery guarantees depend on assumptions that are often too strong in practice. The extension of the mathematical theory as well as the development of new applications in various fields are the subject of many current research activities in the field. The talk will highlight some of the challenges of bridging the gap between theory and practicality of CS.